Invariant solutions, lie symmetry analysis, bifurcations and nonlinear dynamics of the Kraenkel-Manna-Merle system with and without damping effect.

This work investigates the Kraenkel-Manna-Merle (KMM) system, which models the nonlinear propagation of short waves in saturated ferromagnetic materials subjected to an external magnetic field, despite the absence of electrical conductivity. The study aims to explore and derive new solitary wave solutions for this system using two distinct methodological approaches. In the first approach, the KMM system is transformed into a system of nonlinear ordinary differential equations (ODEs) via Lie group transformation. The resulting ODEs are then solved analytically using a similarity invariant approach, leading to the discovery of various types of solitary wave solutions, including bright, dark, and exponential solitons. The second approach involves applying wave and Galilean transformations to reduce the KMM system to a system of two ODEs, both with and without damping effects. This reduced system is further analyzed to investigate its bifurcation behavior, sensitivity to initial conditions, and chaotic dynamics. The analysis reveals the presence of strange multi-scroll chaotic dynamics in the presence of damping and off-boosting dynamics without damping. In addition to these approaches, the study also applies the planar dynamical theory to obtain further new soliton solutions of the KMM system. These solitons include bright, kink, dark, and periodic solutions, each of which has been visualized through 3D and 2D graphs. The results of this research provide new insights into the dynamics of the KMM system, with potential applications in magnetic data storage, magnonic devices, material science, and spintronics.

[How to solve difficult side branch access: case report and literature review]. / Je n'arrive pas à passer mon guide dans la branche fille ; cas clinique et revue de la littérature.

We present the case of a 53-year-old patient with history of hypertension and dyslipidemia, admitted for effort-induced angina. Coronary angiography revealed two-vessel disease with severe stenosis of the LAD- Diagonal bifurcation (MEDINA 1-1-1). This lesion was considered complex regarding the severe stenosis of the bifurcation core, the angulation <45°, and the severity and length of the diagonal lesion. The procedure was planned according to a TAP technique. The flow in the diagonal was however lost after stenting the main vessel causing an ST elevation with chest pain. It was subsequently recovered using the rescue jailed balloon technique before re-crossing the stent struts of the LAD using a Gaia First® (Asahi) guidewire. The aim of this case report is to illustrate some pitfalls that can be encountered in bifurcation percutaneous interventions and to present technical solutions to solve difficult side branch access issues through a literature review.

A geometrical theory of gliding motility based on cell shape and surface flow.

Gliding motility proceeds with little changes in cell shape and often results from actively driven surface flows of adhesins binding to the extracellular environment. It allows for fast movement over surfaces or through tissue, especially for the eukaryotic parasites from the phylum apicomplexa, which includes the causative agents of the widespread diseases malaria and toxoplasmosis. We have developed a fully three-dimensional active particle theory which connects the self-organized, actively driven surface flow over a fixed cell shape to the resulting global motility patterns. Our analytical solutions and numerical simulations show that straight motion without rotation is unstable for simple shapes and that straight cell shapes tend to lead to pure rotations. This suggests that the curved shapes of Plasmodium sporozoites and Toxoplasma tachyzoites are evolutionary adaptations to avoid rotations without translation. Gliding motility is also used by certain myxo- or flavobacteria, which predominantly move on flat external surfaces and with higher control of cell surface flow through internal tracks. We extend our theory for these cases. We again find a competition between rotation and translation and predict the effect of internal track geometry on overall forward speed. While specific mechanisms might vary across species, in general, our geometrical theory predicts and explains the rotational, circular, and helical trajectories which are commonly observed for microgliders. Our theory could also be used to design synthetic microgliders.

Prey group defense and hunting cooperation among generalist-predators induce complex dynamics: a mathematical study.

Group defense in prey and hunting cooperation in predators are two important ecological phenomena and can occur concurrently. In this article, we consider cooperative hunting in generalist predators and group defense in prey under a mathematical framework to comprehend the enormous diversity the model could capture. To do so, we consider a modified Holling-Tanner model where we implement Holling type IV functional response to characterize grazing pattern of predators where prey species exhibit group defense. Additionally, we allow a modification in the attack rate of predators to quantify the hunting cooperation among them. The model admits three boundary equilibria and up to three coexistence equilibrium points. The geometry of the nontrivial prey and predator nullclines and thus the number of coexistence equilibria primarily depends on a specific threshold of the availability of alternative food for predators. We use linear stability analysis to determine the types of hyperbolic equilibrium points and characterize the non-hyperbolic equilibrium points through normal form and center manifold theory. Change in the model parameters leading to the occurrences of a series of local bifurcations from non-hyperbolic equilibrium points, namely, transcritical, saddle-node, Hopf, cusp and Bogdanov-Takens bifurcation; there are also occurrences of global bifurcations such as homoclinic bifurcation and saddle-node bifurcation of limit cycles. We observe two interesting closed 'bubble' form induced by global bifurcations due to change in the strength of hunting cooperation and the availability of alternative food for predators. A three dimensional bifurcation diagram, concerning the original system parameters, captures how the alternation in model formulation induces gradual changes in the bifurcation scenarios. Our model highlights the stabilizing effects of group or gregarious behaviour in both prey and predator, hence supporting the predator-herbivore regulation hypothesis. Additionally, our model highlights the occurrence of "saltatory equilibria" in ecological systems and capture the dynamics observed for lion-herbivore interactions.

Equilibrium bifurcation and extreme risk in the EU carbon futures market.

Considering the long-term memory and volatility clustering of the European Union (EU) Carbon Emission Allowances (EUA) futures returns, based on the economy-energy-environment system perspective and the assumption of investors' heterogeneity, this study proposes a joint modeling approach combining the fractionally integrated generalized autoregressive conditional heteroscedasticity model (FIGARCH) and the stochastic cusp catastrophe model (SCC) to examine the equilibrium bifurcations and extreme risks in the EU carbon futures market. The relevant results are threefold. (1) The SCC model has good fitting effect and interpretability, and is an effective method for investigating catastrophe reactions under time-varying volatility conditions. (2) In the EUA futures market, chartists are mainly affected by short-term price and trading volume changes, which leads to the emergence of equilibrium bifurcations, while fundamentalists make investment decisions based on the economy, the energy market, and market supply-demand, which affects the asymmetry of equilibrium bifurcations. (3) Using the catastrophe criterion (i.e., Cardan's discriminant of the equilibrium surface equation), we identify148 equilibrium bifurcation time points in the EUA futures market from December 3, 2009 to September 16, 2020, most of which are concentrated in two upward periods with an average scale of extreme risks is about 32.51 %. Our analysis provides theoretical support for regulatory authorities to stabilize the carbon futures market and build a collaborative extreme risk management framework covering energy and macroeconomics, also proposing suggestions for traders to effectively prevent extreme risks.

A mathematical model of mobility-related infection and vaccination in an epidemiological case.

In this study, we established a system of differential equations with piecewise constant arguments to explain the impact of epidemiological transmission between different locations. Our main goal is to look into the need for vaccines as well as the necessity of the lockdown period. We proved that keeping social distance was necessary during the pandemic spread to stop transmissions between different locations and that re-vaccinations, including screening tests, were crucial to avoid reinfections. Using the Routh-Hurwitz Criterion, we examined the model's local stability and demonstrated that the system could experience Stationary and Neimark-Sacker bifurcations depending on certain circumstances.

Modeling a SEIVRS dynamic behavior with transportation-related transmissionEstablishing a system of two urban as differential equations with piecewise constant argumentsStability analysis of disease-free and co-existing equilibrium pointsAnalyzing bifurcation types around the disease-free and co-existing equilibrium points.Illustrating numerical scenarios that were applied during the pandemic event.

Weak coupling of neurons enables very high-frequency and ultra-fast oscillations through the interplay of synchronized phase shifts.

Recently, in the past decade, high-frequency oscillations (HFOs), very high-frequency oscillations (VHFOs), and ultra-fast oscillations (UFOs) were reported in epileptic patients with drug-resistant epilepsy. However, to this day, the physiological origin of these events has yet to be understood. Our study establishes a mathematical framework based on bifurcation theory for investigating the occurrence of VHFOs and UFOs in depth EEG signals of patients with focal epilepsy, focusing on the potential role of reduced connection strength between neurons in an epileptic focus. We demonstrate that synchronization of a weakly coupled network can generate very and ultra high-frequency signals detectable by nearby microelectrodes. In particular, we show that a bistability region enables the persistence of phase-shift synchronized clusters of neurons. This phenomenon is observed for different hippocampal neuron models, including Morris-Lecar, Destexhe-Paré, and an interneuron model. The mechanism seems to be robust for small coupling, and it also persists with random noise affecting the external current. Our findings suggest that weakened neuronal connections could contribute to the production of oscillations with frequencies above 1000 Hz, which could advance our understanding of epilepsy pathology and potentially improve treatment strategies. However, further exploration of various coupling types and complex network models is needed.

We have built a mathematical framework to examine how a reduced neuronal coupling within an epileptic focus could lead to very high-frequency (VHFOs) and ultra-fast oscillations (UFOs) in depth EEG signals. By analyzing weakly coupled neurons, we found a bistability synchronization region where in-phase and anti-phase synchrony persist. These dynamics can be detected as very high-frequency EEG signals. The principle of weak coupling aligns with the disturbances in neuronal connections often observed in epilepsy; moreover, VHFOs are important markers of epileptogenicity. Our findings point to the potential significance of weakened neuronal connections in producing VHFOs and UFOs related to focal epilepsy. This could enhance our understanding of brain disorders. We emphasize the need for further investigations of weakly coupled neurons.

From Criegee to Breslow: How π-Donors Steer the Route of Olefin Ozonolysis.

While π-bonds typically undergo cycloaddition with ozone, resulting in the release of much-noticed carbonyl O-oxide Criegee intermediates, lone-pairs of electrons tend to selectively accept a single oxygen atom from O3, producing singlet dioxygen. We questioned whether the introduction of potent electron-donating groups, akin to N-heterocyclic olefins, could influence the reactivity of double bonds - shifting from cycloaddition to oxygen atom transfer or generating lesser-known, yet stabilized, donor-substituted Criegee intermediates. Consequently, we conducted a comparative computational study using density functional theory on a series of model olefins with increasing polarity due to (asymmetric) π-donor substitution. Reaction path computations indicate that highly polarized double bonds, instead of forming primary ozonides in their reaction with O3, exhibit a preference for accepting a single oxygen atom, resulting in a zwitterionic species formally identified as a carbene-carbonyl adduct. This previously unexplored reactivity potentially introduces aldehyde umpolung chemistry (Breslow intermediate) through olefin ozonolysis. Considering solvent effects implicitly reveals that increased solvent polarity further directs the trajectories toward a single oxygen atom transfer reactivity by stabilizing the zwitterionic character of the transition state. The competing modes of chemical reactivity can be explained by a bifurcation of the reaction valley in the post-transition state region.

Efficacy and Safety of Thirty-Day Dual-Antiplatelet Therapy Following Complex Percutaneous Coronary Intervention: A Systematic Review and Meta-Analysis.

The optimal duration of DAPT after complex PCI remains under investigation. The purpose of this systematic review and meta-analysis was to explore the safety and efficacy of a one-month therapy period versus a longer duration of DAPT after complex PCI. We systematically screened three major databases, searching for randomized controlled trials or sub-analyses of them, which compared shortened DAPT (S-DAPT), namely, one month, and longer DAPT (L-DAPT), namely, more than three months. The primary endpoint was any Net Adverse Clinical Event (NACE), and the secondary was any MACE (Major Adverse Cardiac Event), its components (mortality, myocardial infarction, stroke, and stent thrombosis), and major bleeding events. Three studies were included in the analysis, with a total of 6275 patients. Shortening DAPT to 30 days after complex PCI did not increase the risk of NACEs (OR: 0.77, 95% CI: 0.52-1.14), MACEs, mortality, myocardial infractions, stroke, or stent thrombosis. Pooled major bleeding incidence was reduced, but this finding was not statistically significant. This systematic review and meta-analysis showed that one-month DAPT did not differ compared to a longer duration of DAPT after complex PCI in terms of safety and efficacy endpoints. Further studies are still required to confirm these findings.

Optimal dispersal and diffusion-enhanced robustness in two-patch metapopulations: origin's saddle-source nature matters.

A two-patch logistic metapopulation model is investigated both analytically and numerically focusing on the impact of dispersal on population dynamics. First, the dependence of the global dynamics on the stability type of the full extinction equilibrium point is tackled. Then, the behaviour of the total population with respect to the dispersal is studied analytically. Our findings demonstrate that diffusion plays a crucial role in the preservation of both subpopulations and the full metapopulation under the presence of stochastic perturbations. At low diffusion, the origin is a repulsor, causing the orbits to flow nearly parallel to the axes, risking stochastic extinctions. Higher diffusion turns the repeller into a saddle point. Orbits then quickly converge to the saddle's unstable manifold, reducing extinction chances. This change in the vector field enhances metapopulation robustness. On the other hand, the well-known fact that asymmetric conditions on the patches is beneficial for the total population is further investigated. This phenomenon has been studied in previous works for large enough or small enough values of the dispersal. In this work, we complete the theory for all values of the dispersal. In particular, we derive analytically a formula for the optimal value of the dispersal that maximizes the total population.

Dynamical models reveal anatomically reliable attractor landscapes embedded in resting state brain networks.

Analyses of functional connectivity (FC) in resting-state brain networks (RSNs) have generated many insights into cognition. However, the mechanistic underpinnings of FC and RSNs are still not well-understood. It remains debated whether resting state activity is best characterized as noise-driven fluctuations around a single stable state, or instead, as a nonlinear dynamical system with nontrivial attractors embedded in the RSNs. Here, we provide evidence for the latter, by constructing whole-brain dynamical systems models from individual resting-state fMRI (rfMRI) recordings, using the Mesoscale Individualized NeuroDynamic (MINDy) platform. The MINDy models consist of hundreds of neural masses representing brain parcels, connected by fully trainable, individualized weights. We found that our models manifested a diverse taxonomy of nontrivial attractor landscapes including multiple equilibria and limit cycles. However, when projected into anatomical space, these attractors mapped onto a limited set of canonical RSNs, including the default mode network (DMN) and frontoparietal control network (FPN), which were reliable at the individual level. Further, by creating convex combinations of models, bifurcations were induced that recapitulated the full spectrum of dynamics found via fitting. These findings suggest that the resting brain traverses a diverse set of dynamics, which generates several distinct but anatomically overlapping attractor landscapes. Treating rfMRI as a unimodal stationary process (i.e., conventional FC) may miss critical attractor properties and structure within the resting brain. Instead, these may be better captured through neural dynamical modeling and analytic approaches. The results provide new insights into the generative mechanisms and intrinsic spatiotemporal organization of brain networks.

Investigating the impact of vaccine hesitancy on an emerging infectious disease: a mathematical and numerical analysis.

Throughout the last two centuries, vaccines have been helpful in mitigating numerous epidemic diseases. However, vaccine hesitancy has been identified as a substantial obstacle in healthcare management. We examined the epidemiological dynamics of an emerging infection under vaccination using an SVEIR model with differential morbidity. We mathematically analyzed the model, derived R0, and provided a complete analysis of the bifurcation at R0=1. Sensitivity analysis and numerical simulations were used to quantify the tradeoffs between vaccine efficacy and vaccine hesitancy on reducing the disease burden. Our results indicated that if the percentage of the population hesitant about taking the vaccine is 10%, then a vaccine with 94% efficacy is required to reduce the peak of infections by 40%. If 60% of the population is reluctant about being vaccinated, then even a perfect vaccine will not be able to reduce the peak of infections by 40%.

Dynamics aspects and bifurcations of a tumor-immune system interaction under stationary immunotherapy.

We consider a three-dimensional mathematical model that describes the interaction between the effector cells, tumor cells, and the cytokine (IL-2) of a patient. This is called the Kirschner-Panetta model. Our objective is to explain the tumor oscillations in tumor sizes as well as long-term tumor relapse. We then explore the effects of adoptive cellular immunotherapy on the model and describe under what circumstances the tumor can be eliminated or can remain over time but in a controlled manner. Nonlinear dynamics of immunogenic tumors are given, for example: we prove that the trajectories of the associated system are bounded and defined for all positive time; there are some invariant subsets; there are open subsets of parameters, such that the system in the first octant has at most five equilibrium solutions, one of them is tumor-free and the others are of co-existence. We are able to prove the existence of transcritical and pitchfork bifurcations from the tumor-free equilibrium point. Fixing an equilibrium and introducing a small perturbation, we are able to show the existence of a Hopf periodic orbit, showing a cyclic behavior among the population, with a strong dominance of the parental anomalous growth cell population. The previous information reveals the effects of the parameters. In our study, we observe that our mathematical model exhibits a very rich dynamic behavior and the parameter µÌƒ (death rate of the effector cells) and p̃1 (production rate of the effector cell stimulated by the cytokine IL-2) plays an important role. More precisely, in our approach the inequality µÌƒ2>p̃1 is very important, that is, the death rate of the effector cells is greater than the production rate of the effector cell stimulated by the cytokine IL-2. Finally, medical implications and a set of numerical simulations supporting the mathematical results are also presented.

Modeling the impact of hospital beds and vaccination on the dynamics of an infectious disease.

The unprecedented scale and rapidity of dissemination of re-emerging and emerging infectious diseases impose new challenges for regulators and health authorities. To curb the dispersal of such diseases, proper management of healthcare facilities and vaccines are core drivers. In the present work, we assess the unified impact of healthcare facilities and vaccination on the control of an infectious disease by formulating a mathematical model. To formulate the model for any region, we consider four classes of human population; namely, susceptible, infected, hospitalized, and vaccinated. It is assumed that the increment in number of beds in hospitals is continuously made in proportion to the number of infected individuals. To ensure the occurrence of transcritical, saddle-node and Hopf bifurcations, the conditions are derived. The normal form is obtained to show the existence of Bogdanov-Takens bifurcation. To validate the analytically obtained results, we have conducted some numerical simulations. These results will be useful to public health authorities for planning appropriate health care resources and vaccination programs to diminish prevalence of infectious diseases.

Pseudo-nullclines enable the analysis and prediction of signaling model dynamics.

A powerful method to qualitatively analyze a 2D system is the use of nullclines, curves which separate regions of the plane where the sign of the time derivatives is constant, with their intersections corresponding to steady states. As a quick way to sketch the phase portrait of the system, they can be sufficient to understand the qualitative dynamics at play without integrating the differential equations. While it cannot be extended straightforwardly for dimensions higher than 2, sometimes the phase portrait can still be projected onto a 2-dimensional subspace, with some curves becoming pseudo-nullclines. In this work, we study cell signaling models of dimension higher than 2 with behaviors such as oscillations and bistability. Pseudo-nullclines are defined and used to qualitatively analyze the dynamics involved. Our method applies when a system can be decomposed into 2 modules, mutually coupled through 2 scalar variables. At the same time, it helps track bifurcations in a quick and efficient manner, key for understanding the different behaviors. Our results are both consistent with the expected dynamics, and also lead to new responses like excitability. Further work could test the method for other regions of parameter space and determine how to extend it to three-module systems.

Mathematical birth of Early Afterdepolarizations in a cardiomyocyte model.

Early Afterdepolarizations (EADs) are abnormal behaviors that can lead to cardiac failure and even cardiac death. In this paper we investigate the occurrence and development of these phenomena in a reduced Luo-Rudy cardiac model. Through a comprehensive dynamical analysis, we map out the distinct patterns observed in the parametric plane, differentiating between normal beats without EADs and pathological beats with EADs. By examining the bifurcation structure of the model, we elucidate the dynamical elements associated with these patterns and their transitions. Using a fast-slow analysis, we explore the emergence and evolution of EADs in the model. Notably, our approach combines the two commonly used fast-slow approaches (1-slow-2-fast and 2-slow-1-fast), and we show how both approaches together provide a more complete understanding of this phenomenon.

Nonlinear Dynamic Analysis of an Electrostatically Actuated Clamped-Clamped Beam and Excited at the Primary and Secondary Resonances.

This work investigates the primary and secondary resonances of an electrostatically excited double-clamped microbeam and its feasibility to be used for sensing applications. The sensor design can be excited directly in the vicinity of the primary and secondary resonances. This excitation mechanism would portray certain nonlinear phenomena and it would certainly lead in increasing the sensitivity of the device. To achieve this, a nonlinear beam model describing transverse deflection based on the Euler-Bernoulli beam theory was utilized. Then, a reduced-order model (ROM) considering all geometric and electrical nonlinearities was derived. Three different techniques involving time domain, fast Fourier transforms (FFTs), and frequency domain (FRCs) were used to examine the appearance of subharmonic resonance of order of one-half under various excitation waveforms. The results show that higher forcing levels and lower damping are required to activate this resonance. We note that as the forcing increases, the size of the instability region grows fast and the size of the unstable region increases rapidly. This, in fact, is an ideal place for designing bifurcation inertia MEMS sensors.

The Information Bottleneck's Ordinary Differential Equation: First-Order Root Tracking for the Information Bottleneck.

The Information Bottleneck (IB) is a method of lossy compression of relevant information. Its rate-distortion (RD) curve describes the fundamental tradeoff between input compression and the preservation of relevant information embedded in the input. However, it conceals the underlying dynamics of optimal input encodings. We argue that these typically follow a piecewise smooth trajectory when input information is being compressed, as recently shown in RD. These smooth dynamics are interrupted when an optimal encoding changes qualitatively, at a bifurcation. By leveraging the IB's intimate relations with RD, we provide substantial insights into its solution structure, highlighting caveats in its finite-dimensional treatments. Sub-optimal solutions are seen to collide or exchange optimality at its bifurcations. Despite the acceptance of the IB and its applications, there are surprisingly few techniques to solve it numerically, even for finite problems whose distribution is known. We derive anew the IB's first-order Ordinary Differential Equation, which describes the dynamics underlying its optimal tradeoff curve. To exploit these dynamics, we not only detect IB bifurcations but also identify their type in order to handle them accordingly. Rather than approaching the IB's optimal tradeoff curve from sub-optimal directions, the latter allows us to follow a solution's trajectory along the optimal curve under mild assumptions. We thereby translate an understanding of IB bifurcations into a surprisingly accurate numerical algorithm.

The Dynamics of Pasture-Herbivores-Carnivores with Sigmoidal Density Dependent Harvesting.

We investigate biomass-herbivore-carnivore (top predator) interactions in terms of a tritrophic dynamical systems model. The harvesting rates of the herbivores and the top predators are described by means of a sigmoidal function of the herbivores density and the top predator density, respectively. The main focus in this study is on the dynamics as a function of the natural mortality and the maximal harvesting rate of the top predators. We identify parameter regimes for which we have non-existence of equilibrium points as well as necessary conditions for the existence of such states of the modelling framework. The system does not possess any finite equilibrium states in the regime of high herbivore mortality. In the regime of a high consumption rate of the herbivores and low mortality rates of the top predator, an asymptotically stable finite equilibrium state exists. For this positive equilibrium to exist the mortality of the top predator should not exceed a certain threshold level. We also detect regimes producing coexistence of equilibrium states and their respective stability properties. In the regime of negligible harvesting of the top predator level, we observe a finite window of the natural top predator mortality rates for which oscillations in the top predator-, the herbivore- and the biomass level take place. The lower and upper bound of this window correspond to two Hopf bifurcation points. We also identify a bifurcation diagram using the top predator harvesting rate as a control variable. Using this diagram we detect several saddle node- and Hopf bifurcation points as well as regimes for which we have coexistence of interior equilibrium states, bistability and relaxation type of oscillations.

Applications of the generalized gamma function to a fractional-order biological system.

In this work, variety of complex dynamics are found in a fractional-order antimicrobial resistance (AMR) model based on the generalized Gamma function. Firstly, the extended left and right Caputo fractional differential operators, respectively, ELCFDO and ERCFDO are introduced. The basic features of the ELCFDO are outlined. The ELCFDO is shown to have a new fractional parameter that affects the occurrence of the complex dynamics in the fractional AMR system. Secondly, discretization of the ELCFDO is studied using piecewise constant arguments. Then, complex dynamics of the discretized version of the fractional AMR system involving the ELCFDO are investigated such as the existence of Neimark-Sacker (NS) and flip bifurcations, the existence of closed invariant curves (CIC), the existence of strange attractors with fractal or multi-fractal structures, and chaotic attractors. Finally, an extension of the fractal-fractional operator (FFO) that combines fractal and fractional differentiation is carried out based on the generalized Gamma function. The extended FFO (EFFO) is applied to the proposed AMR system, which also generates similar complex dynamics.